In the distribution of electrical energy, electric utility companies have typically found it desirable to measure quantities related to the delivery of electrical energy to a consumer which accurately reflect the cost of delivering that energy to that consumer, and thus equitably apportion the cost of delivering energy among all the users of the power system. Early on, utilities realized that billing customers based merely upon measurement of actual energy delivered --Watt-hours--fails to accurately reflect the cost of delivering energy to the customer. For example, large industrial users may have inductive loads, such as large induction motors, which induce significant phase shifts between voltages and currents in the power line, thus requiring advancement of generator angles and capacitive compensation by the utility in order to maintain voltage levels efficiently deliver energy to consumers and preserve stability in the power system. This added generation and capital equipment cost is not reflected in measurements of energy delivered at the customer metering point.
Accordingly, other measures of electric power have been developed. For example, utilities typically bill not only for real load energy as watthours delivered to a user, but also reactive load quadergy as varhours (or reactive volt-ampere hours) and power factor (cos .theta.) by measuring both watthours and varhours electric utilities can more accurately apportion the costs of supplying energy to those customers with inductive loads which demand the most from the power delivery network.
Potential errors in power measurement attributable to nonsinusoidal conditions were also recognized early in this century. Nearly sixty years ago, power systems engineers attempted to develop a general unified theoretical model for power systems which accounts for harmonics and distortion. This model is described in an article, "Definitions of Power and Related Quantities" by Harvey L. Curtis and Francis S. Silsbee of the National Bureau of Standards, published for the 1935 AIEE Summer Conference. The definitions in the Curtis and Silsbee article are derived from a three-dimensional vector model of electrical power applicable for all harmonics and phases. These definitions have survived largely intact through the publication of the latest editions of the "IEEE Std 100, Standard Dictionary of Electrical and Electronic Terms."
Power vector relationships for a power line are illustrated in FIG. 19. The ANSI/IEEE STD 100 Dictionary of Electrical and Electronic Terms defines "phasor power" S as the magnitude of a two-dimensional power vector whose rectangular components are "active power" P and "reactive power" Q. In systems of more than one conducting path, i.e., "polyphase" systems and "single-phase" systems with more than one conducting path, phasor power S is the vector sum of active power P and reactive power S for the system, for all harmonics. As will be understood by those skilled in the art, phasor power S is equal to active power P when all load elements are resistive. In one form or another, it is phasor power, or more specifically, phasor volt-ampere hours, which utilities have traditionally metered and billed. Typically, utilities have measured phasor volt-ampere-hours for the fundamental frequency of the system voltage using conventional watthour meters and varhour meters.
"Apparent power" U is defined as the magnitude of a three-dimensional vector power with orthogonal components of active power P, reactive power Q and a third component, "distortion power" D. Apparent power and apparent volt-ampere-hours provide a more comprehensive measure of the characteristics of a power line. For an isolated two-terminal circuit, apparent power U may be treated as a scalar, the product of the root-mean-square voltage and current in the single conducting path. In a system having more than one conducting wire, however, vector apparent power and vector apparent volt-ampere-hours are vectors, the vector sum of real, reactive and distortion power components for all phases and harmonics. For this reason, vector apparent power and vector apparent volt-ampere-hours have been largely ignored as practical metering quantities because of a lack of techniques to accurately measure their vector components. Instead, utilities have relied on alternative measurements such as quadergy and phasor volt-ampere-hours, for which measurement techniques and equipment could be easily developed.
Conventional sampling electronic watthour meters generally accurately measure energy by accumulating instantaneous power measurements. This is typically achieved by sampling voltage and current on the power line and converting the sampled voltages and currents into digital values which may be multiplied to compute the instantaneous power. These sampling products are accumulated to yield a measurement of energy transferred by the power line, which can be inherently accurate for all significant harmonics assuming the sampling rate satisfies the sampling theorem. As defined in ANSI/IEE STD 100-1992, apparent power for a two terminal circuit is: EQU U.sub.X =E.sub.rms.times.I.sub.rms
where E.sub.rms and I.sub.rms are the root-mean-square values of the voltage and current for the circuit. Thus, viewing voltage and currents on a power line as a composite of sinusoidal signals, apparent power (or apparent volt-ampere-hours) for all harmonics on a phase of a power line may be determined by measuring RMS voltage and current.
Measurement of quadergy, however, is more problematic. The measurement of varhours conventionally has been accomplished either by using a second meter in conjunction with a conventional watthour meter or, more recently, a meter with the built-in capability of measuring both watthours and varhours. Typically, the technique for measuring varhours involves phase-shifting the measured line voltage by 90.degree. using phase-shifting transformers (in analog meters) or time delay elements (in digital meters). Both of these methods may entail significant errors arising from disregarding or failing to accurately shift all the significant harmonics of the voltage.
Metering based on arithmetic apparent volt-ampere-hours for the power line has been proposed as an approximation of vector apparent volt-ampere-hours. Arithmetic apparent power for a multi-phase system represents the arithmetic sum of the magnitude of the apparent power for each of the individual phases. Although relatively easy to compute, arithmetic apparent power tends to closely approximate vector apparent power only in cases where the phases of the power line are balanced and symmetric. Even in those cases, its measurement often leads to unexpected results under certain circumstances where the current or voltage waveforms are nonsinusoidal. These characteristics tend to make arithmetic apparent power an unsuitable quantity for electrical metering.
Conventional electricity meters and metering methods may fail to provide accurate measurement of the actual cost of providing electrical energy to consumers where distortion is present. increasing use of solid state switched motor drives, large switching power supplies and switched loads such as computers lead to distorted current waveforms, generally accompanied by a greater amount of associated distortion power. Distortion power increases demand on utility equipment and increases energy losses. Measures such as phasor volt-ampere-hours and arithmetic apparent volt-ampere-hours fail to rationally reflect these associated costs.
Errors arising from use of these conventional measurement techniques will become increasingly significant as the cost of delivering energy increases. Utilities, driven by costs and the demands of their customers for billing equity, have an increasing need for accurate metering which reflects the true cost of delivering energy. In order to provide continuity and minimize replacement costs, however, new equipment and methods should be compatible with conventional meter connections and conventional metering formats, as well as with the various circuit topologies employed in electrical services.